[学习指导] 南外小升初数学冲刺班补充习题.pdf

学理科到学而思 1 学而思南外冲刺数学模拟试题 1 Which of the following is the largest A 105 2 3 B 17 2 C 8 4 D 7 6 E 9 3 2 The planet Pluto has 3 moons Moon 1 takes 6 days to make a complete revolution around the planet moon 2 takes 10 days and moon 3 takes 15 days Staring from the position shown on the diagram how many days are necessary to retum to the original position A 30days B 60days C 90days D 150days E 900days 3 A and B are the middle points of the sides What fraction of the total area does the shaded region represen A 1 16 B 1 8 C 1 4 D 1 3 E None of these 4 All the positive integers less than 49 are multiplied together How many zeros will this product end in A 5 B 9 C 10 D 48 E 49 5 Six years ago Samuel was 3 5 of his current age How old is Samuel now A 15 B 21 C 25 D 30 E None of these 6 If 130 142 x x what is the value of x A 4 B 5 C 6 D 7 E 31 7 What is the next number in the squence 2 1 3 4 7 11 A 10 B 12 C 15 D 18 E 22 8 How many different squares are there in the figure shown at right A 19 B 20 C 21 D 22 E 23 P 3 2 1 学理科到学而思 2 9 Four tennis players enter a tournament How many different ways can the pairings be made for the first round games A 3 B 6 C 8 D 12 E 24 10 A 4 4 4 cube consisting of smaller cubes is painted and then broken apart How many of the smaller cubes will have exactly 2 painted sides A 8 B 16 C 20 D 24 E 32 11 For a party Justin buys a pizza and cuts it into 24 pieces Marc eats 1 6 of the pizza and Claudine eats 1 4 of what remains After both of them have eaten Sylvie eats 1 3 of the rest Justin gets to eat what is left over What fraction of the pizza did Justin not eat A 1 2 B 5 12 C 7 12 D 2 3 E None of these 12 How many trangles are contained in this figure A 16 B 17 C 24 D 26 E 27 13 A clock is set correctly at 1 00p m It loses 3 minutes duning every hour What will the clock read when the correct time is 10 00a m the next day A 8 57 B 9 03 C 10 00 D 11 03 E None of these 14 In a tournament where each team meets every other team twice a total of 30 games are played How many teams play in this tournament A 4 B 5 C 6 D 7 E 15 15 How many integers n are there such that 5113 6157n A 1 B 6 C 7 D 8 E 9 16 Of the following which is the closest estimate of 1997 10000 A 0 0044 B 0 0141 C 0 0446 D 0 1411 E 0 4469 学理科到学而思 3 17 Find the missing term in the sequence 1 2 5 12 58 A 24 B 27 C 28 D 33 E None of these 18 What is the area of the shaded region A 6 B 8 C 10 D 12 E Not enough information 19 You are given a set of three numbers If the numbers are added together two at a time the sums are 23 32and 39 What is the sum of the three numbers A 44 B 47 C 50 D 94 E None of these 20 In the diagram line segments meet at 90 as shown If the short line segments are each 3 cm long what is the area of the shape A 30 B 36 C 40 D 45 E 54 21 A box contains 36 pink 18 blue 9 green 6 red and 3purple cubes that are identical in size If a cube is selected at random what is the probability that it is green A 1 9 B 1 8 C 1 5 D 1 4 E 9 70 22 The graph shown at the right indicates the time taken by five people to travel various distances On average which person travelled the fastest A Alison B Bina C Curtis D Daniel E Emily 2 2 32 1 3cm 学理科到学而思 4 23 What is the area in 2 m of the shaded part of the rectangle A 14 B 28 C 33 6 D 56 E 42 24 A game is played on the board shown In this game a player can move three places in any direction up down right or left and then can move two places in a direction perpendicular to the first move If a player starts at S which position on the board P Q R T or W cannot be reached through any sequence of moves A P B Q C R D T E W 25 JKLM is a square Points P and Q are outside the square such that triangles JMP and MLQ are both equilateral The size in degrees of angle PQM is A 10 B 15 C 25 D 30 E 150 Curtis Alison Emily Daniel Bina Time minute 10 20 30 40 50 Distance kilometres 1 2 3 4 5 14米 4米 WS T RQ P 学理科到学而思 5 26 A different letter is painted on each face of a cube This cube is shown below in 3 different positions What letter belongs on the shaded face of this cube in the following diagram A T B P C X D E E V 27 The digits 1 2 3 4 5 and 6 are each placed in one of the boxes so that the resulting product is correct If each of the xis digits is used exactly once the digit represented by is A 2 B 3 C 4 D 5 E 6 28 A rectangular wooden prism is made up of three pieces each consisting of four cubes of wood glued together Which of the pieces below has the same shape as the black piece LK Q M J P 学理科到学而思 6 29 The area of square ABCD is 64 and 2AXBWCZDY What is the area of square WXYZ A 58 B 52 C 48 D 40 E 36 30 In an 2004 Olympics there are six competitors and eight events The top three competitors in each event receive gold silver and bronze medals respectively There are no ties at the Olympics and no competitor can win more than one medal on the same event Each competitor scores 5 points for each gold medal 3 points for each silver medal and 1 point for each bronze medal If one of the competitors had a total of 27 points what is the maxmum number of silver medals she could have won A 6 B 2 C 3 D 4 E 5 31 Paul Quincy Rochelle Surinder and Tony are sitting around a table Quincy sits in the chair between Paul and Surinder Tony is not beside Surinder Who is sitting on either side of Tony A Paul and Rochelle B Quincy and Rochelle C Paul and Quincy D Surinder and Quincy E Not possible to tell 32 The month of April 2000 had five Sundays Three of them fall on even numbered days The eighth day of this month is a D E A B C Z X D Y C A W B 学理科到学而思 7 A Saturday B Sunday C Monday D Tuesday E Friday 33 The diagram shows two isosceles right rtiangles with sides as marked What is the area of the shaded region A 2 4 5cm B 2 8cm C 2 12 5cm D 2 16cm E 2 17cm 34 BC is a diameter of the circle with centre O and radius 5 as shown If A lies on the circle and AO is perpenclicular to BC the area of triangle ABC is A 6 25 B 12 5 C 25 D 37 5 E 50 35 The figure shown can be folded along the lines to form a rectargular prisrn The surface area of the rectangular prism in 2 cm is A 312 B 300 C 280 D 84 E 600 36 In the multiplication question the sum of the digits in the four boxes is A 13 B 12 C 27 D 9 E 22 3cm 5cm 5O CB A 5cm 6cm 10cm 879 492 758 7 11 35 6 43 468 学理科到学而思 8 37 Kalyn cut rectangle R from a sheet of paper A smaller rectangle is then cut from the large rectangle R to produce figure S In comparing R to S A the area and perimeter both decrease B the area decreascs and the perimeter increases C the area and perimeter both increase D the area increases and the perimeter decreases E the area decreases and the perimeter stays the same 38 The pattern of figures is repeated in the sequence The 214th figure in the sequence is A B C D E 39 Claire takes a square piece of paper and folds it in half four time without unfolding making an isosceles right triangle each time After unfolding the paper to form a square again the creases on the paper would look like 40 The volume of the solid figure shown is A 12 B 30 C 35 D 36 E 40 6cm 4cm 5cm 6cm 8cm 8cm 8cm S R D E A B C 2 5 3 1 2 学理科到学而思 9 41 Mr Martin bought two balls which he then resold at 1 20each Hased on the cost of the balls the price he payed Mr Martin made a profit of 20 on one of the balls and encountered a loss of 20 on the orher Overall both sales have led to A no net profit B a loss of 4 cents C a profit of 4 cents D a loss of 10 cents E a profit of 10 cents 42 Which of the following expressions is the largest A 1 B 1 11 23 C 3 1 1 10 D 1 1 6 1 1 6 E 3 1 1 10 43 If our days were divided into 10 hours with no need for a m and p m the new hours into 100 minutes and the new minutes into 100 seconds what new time would it be at 6 p m A 6 00 B 6 48 C 7 00 D 9 00 E None of these 44 The map shows the cost of travelling through each section of road What is the lowest possible cost for going from point A to point B A 17 B 18 C 19 D 20 E 21 45 Which of the squares A B CorDshould logically occupy the missing place in the figure below A B C D E Not enough information 1 2 6 7 5 4 2 8 7 1 6 6 4 5 5 7 3 B A 学理科到学而思 10 46 Observe 1 5 1 52 25 2 5 2 56 25 3 5 3 512 25 The value of if 9900 25 is A 33 5 B 66 5 C 99 5 D 100 5 E 300 5 47 What is the remainder when 2030 3 42 is divided by 12 A 1 B 2 C 4 D 9 E 10 48 The value of the expression 1 2345678976777879 is equal to A 98 B 80 C 60 D 40 E 80 49 What is the last digit of 2002 3 A 1 B 3 C 5 D 7 E 9 50 The mathematician Augustus De Morgan lived in the nineteenth century He once made the following statement I was x years old in the year 2 x In what year was De Morgan bom A 1801 B 1806 C 1849 D 1860 E None of these 51 Find the sum of all the integers x for which 1 2000520000 x 52 The value of 22222222 1009896948642 is 53 What is the remainder when 13 6 is divided by 7 54 What fraction of the area of the large triangle is shaded 55 A set of 1 1 1 cubes is used to construct a hollow 10 10 10 cube whose shell is two layers of cubes in thickness How many cubes are needed 56 The cities of A and B are a distance of 500 km from each other An airplane regularly makes a round trip between them The wind always blows at a constant 1 1 2 1 学理科到学而思 11 velocity from A towards B The speed of the airplane unmodified by the wind is 900km h If the trip from A to B takes 30 minutes and the return trip takes 1 37 2 minutes what is the velocity of the wind 57 An inheritance is split among 5 brothers The first receives half of the inheritance plus 1 The second receives half of the remainder plus 2 The third receives half of the remainder plus 3 The fourth receives half of the remainder plus 4 The last brother receives 500 What is the total amount of the inheritance 58 How many distinct paths lead from A to B if the only possible directions are to go forward to the north the east or the north east 59 In a woodlot a forest engineet has found that 3000 trees are ready for cutting In this woodlot 40 of the trees are conifers and 60 are leafy trees Also 62 of the leafy trees are maples while 25 of the conifers are pines Altogether how many maples and pines can be cut 60 A solid cube with 3 metre side lengths has square holes cut through it from the middle of each face to the middle of the opposite face as shown The three holes intersect in the middle of the cube The square windows so produed have side lengths of 1 metre each What is the total surface area in square metres of the new solid 61 What is the next number in the sequence 1 2 3 4 6 9 13 19 28 A B WE N S 3m 3m 1m 3m 学理科到学而思 12 62 Using coins with values of 1 5 10 and 25 what is the smallest number of coins needed to be able to exactly make each to tal from 1 to 1 00 63 E F G and H are the middle points of the sides of rectangle ABCD and K is the middle point of segment HE If the rectangle ABCD has an area of 2 12m what is the area of the triangle KFG 64 Four identical isosoeles triangles border a square of side 6 cm as shown When the four triangles are folded up they meet at a point to form a pyamid with a square base If the height of this pyramid is 4 cm the total area of the four triangles and the square is 65 The table to the right shows the high and low temperatures recorded in a city last week On what day was the temperature range the greates Day High Temperature Low Temperature Monday 5 3 Tuesday 0 10 Wednesday 2 11 Thursday 8 13 Friday 7 9 66 Two fair coins are tossed at the same time What is the probability they will both AEB CGD H K F 6cm 学理科到学而思 13 land as HEADS 67 The prime numbers between 10 and 20 are added together to form the number Q What is the largest prime divisor of Q 68 If Tom walks to school and rides his bicycle back home it takes him 90 minutes If he rides his bicycle both ways it takes him 30 minutes How many hours would it take him to make the trip to school and back by walking Assume that he walks at a constant speed and that he cycles at a constant speed 69 Jim drives 60 km south 40 km west 20 km north and 10 km east What is the distance from his starting point to his finishing point 70 The cookies in a jar contain a total of 1000 chocolate chips All but one of these cookines contairs the same number of chips it contairs one more chip than the others The number of cookies in the jar is between one dozen and three dozen What is the sum of the number of cookies in the jar and the number of chips in the cookie with the extra chocolate chip 71 In a class of 25 students each student has at most one pet Three fifths of the students have cats 20 have dogs three have elephants and the other students have no pets How many students have no pets 72 Daniel s age is one ninth of his father s age One year from now Daniel s father s age will be seven times Daniel s age The difference between their age is 73 The integers 2 2 5 5 8 and 9 are written on six cards as shown Any number of the six cards is chosen and the sum of the integers on these cards is determined Note that the integers 1 and 30 cannot be obtained as sums in this way How many of the integers from 1 to 31 cannot be obtained as sums 74 Tony and Maria are training for a race by running all the way up and down a 700 m long ski slope They each run up the slope at different constant speeds Coming down the slope each runs at double his or her uphill speed Maria reaches the top first and immediately starts running back down meeting Tony 70 m from the top When Maria reaches the bottom how far behind is Tony 75 The diagram shows 4 bricks enclosing a square Each brick has length 18 and 学理科到学而思 14 breadth 10 The length of the side of the enclosed square is 76 Emily has created a jumping game using a straight row of floor tiles that she has numbered 1 2 3 4 Starting on tile 2 she jumps along the row landing on every second tile and stops on the second last tile in the row Starting from this tile she turns and jumps back toward the start this time landing on every third tile She stops on tile 1 Finally she turns again and jumps along the row landing on every fifth tile This time she again stops on the second last tile The number of tiles in the row could be 77 Emily sits on a chair in a room Behind her is a clock In front of her is a mirror In the mirror she sees the image of the clock as shown The actual time is closest to 78 A regular pentagon has all sides and angles equal If the shaded pentagon is enclosed by squares and triangles as shown what is the size of angle x 79 A slow train travelling from A city to B city arrives 9 minutes late when travelling at 36 km h If it travels at 27 km h it arrives 39 minutes late Whet is the distance between A city and B city x 学理科到学而思 15 80 Triangle ABC has an area of 25 2 m If a larger triangle ABC is formed as shown knowing that the lengths ABAB CBBC and CAAC what is the area of triangle ABC 81 How many black tiles will be required to build the 15th figure in the given pattern 82 In a group of men and women the average age is 31 If the men s ages average 35 years and the women s ages average 25 then the ratio of the number of men to the number of women is 83 I have 6 different books 3 with red covers and 3 with blue covers In how many different ways can I arrange these books on a shelf so that no two books of the same colour are next to cach other 84 The average of the first 100 000 odd positive in tegers is 85 The homes of Fred F Sandy S Robert R and Guy G are marked on the rectangular grid with straight lines joining them Fred is considering four routes to visit each of his friends FRSG FSGR FRGS FSRG If 5kmFS 9kmSG and 12kmSR the difference between the longest and the shortest trip in km is A B C A B C 1st 2nd 3rd 5th 学理科到学而思 16 86 How many fractions whose denominator is 23 have values between 0 18